Stochastic models of Mendelian and reverse transcriptional inheritance in state-structured cancer populations

Modeling stress-induced responses: plasticity in continuous state space and gradual clonal evolution

Mathematical models of cancer and bacterial evolution have generally stemmed from a gene-centric framework, assuming clonal evolution via acquisition of resistance-conferring mutations and selection of their corresponding subpopulations. More recently, the role of phenotypic plasticity has been recognized and models accounting for phenotypic switching between discrete cell states (e.g., epithelial and mesenchymal) have been developed. However, seldom do models incorporate both plasticity and mutationally driven resistance, particularly when the state space is continuous and resistance evolves in a continuous fashion. In this paper, we develop a framework to model plastic and mutational mechanisms of acquiring resistance in a continuous gradual fashion. We use this framework to examine ways in which cancer and bacterial populations can respond to stress and consider implications for therapeutic strategies. Although we primarily discuss our framework in the context of cancer and bacteria, it applies broadly to any system capable of evolving via plasticity and genetic evolution.

A mathematical investigation of polyaneuploid cancer cell memory and cross-resistance in state-structured cancer populations

The polyaneuploid cancer cell (PACC) state promotes cancer lethality by contributing to survival in extreme conditions and metastasis. Recent experimental evidence suggests that post-therapy PACC-derived recurrent populations display cross-resistance to classes of therapies with independent mechanisms of action. We hypothesize that this can occur through PACC memory, whereby cancer cells that have undergone a polyaneuploid transition (PAT) reenter the PACC state more quickly or have higher levels of innate resistance. In this paper, we build on our prior mathematical models of the eco-evolutionary dynamics of cells in the 2N+ and PACC states to investigate these two hypotheses. We show that although an increase in innate resistance is more effective at promoting cross-resistance, this trend can also be produced via PACC memory. We also find that resensitization of cells that acquire increased innate resistance through the PAT have a considerable impact on eco-evolutionary dynamics and extinction probabilities. This study, though theoretical in nature, can help inspire future experimentation to tease apart hypotheses surrounding how cross-resistance in structured cancer populations arises.

Mathematical Modeling of Field Cancerization through the Lens of Cancer Behavioral Ecology

Field cancerization is a process in which a normal tissue is replaced with pre-cancerous but histologically normal tissue. This transformed field can give rise to malignancy and contribute to tumor relapse. In this paper, we create a mathematical model of field cancerization from the perspective of cancer behavioral ecology. In our model, field cancerization arises from a breakdown in signaling integrity and control, and investigate implications for acute wounding, chronic wounding, aging, and therapeutic interventions. We find that restoration of communication networks can lead to cancer regression in the context of acute injury. Conversely, long term loss of controls, such as through chronic wounding or aging, can promote oncogenesis. These results are paralleled in therapeutic interventions: those that simply target cells in cancerous states may be less effective than those that reestablish signaling integrity. Viewing cancer as a corruption of communication systems rather than as a corruption of individual cells may lead to novel approaches for understanding and treating this disease.